Optimal Transport-Based Clustering of Attributed Graphs with an Application to Road Traffic Data

TL;DR

This paper introduces optimal transport-based clustering methods for attributed graphs, specifically applied to road traffic data, effectively combining structural and attribute information to identify meaningful network clusters.

Contribution

It adapts Gromov--Wasserstein methods for attributed graph partitioning, providing theoretical guarantees and handling heterogeneous attributes, with practical evaluation on real-world traffic data.

Findings

GW methods effectively leverage structure and attributes

Proposed methods show robustness to noise

Enhanced clustering performance with distance-based embeddings

Abstract

In many real-world contexts, such as social or transport networks, data exhibit both structural connectivity and node-level attributes. For example, roads in a transport network can be characterized not only by their connectivity but also by traffic flow or speed profiles. Understanding such systems therefore requires jointly analyzing the network structure and node attributes, a challenge addressed by attributed graph partitioning, which clusters nodes based on both connectivity and attributes. In this work, we adapt distance-based methods for this task, including Fr\'echet $k$-means and optimal transport-based approaches based on Gromov--Wasserstein (GW) discrepancy. We investigate how GW methods, traditionally used for general-purpose tasks such as graph matching, can be specifically adapted for node partitioning, an area that has been relatively underexplored. In the context of node-attributed graphs, we introduce an adaptation of the Fused GW method, offering theoretical guarantees and the ability to handle heterogeneous attribute types. Additionally, we propose to incorporate distance-based embeddings to enhance performance. The proposed approaches are systematically evaluated using a dedicated simulation framework and illustrated on a real-world transportation dataset. Experiments investigate the influence of target choice, assess robustness to noise, and provide practical guidance for attributed graph clustering. In the context of road networks, our results demonstrate that these methods can effectively leverage both structural and attribute information to reveal meaningful clusters, offering insights for improved network understanding.